In order to deduce their structure-function relationships, respiratory hemoproteins such as myoglobin, hemoglobin, and cytochrome from different sources will be selectively modified at their specific molecular moieties and the physical and chemical properties of such modified hemoproteins will be examined by thermodynamic and kinetic measurements of their ligand equilibria and EPR, NMR, resonance Raman, Mossbauer, EXAFS, and infrared spectroscopic and x-ray crystallographic characterizations of their unligated, fully ligated, and partially ligated states. The prosthetic groups of respiratory hemoproteins, particularly myoglobin and hemoglobin (FeMb and FeHb), are chemically exchanged with cobaltous porphyrins to form cobalt-substituted myoglobin and hemoglobin (CoMb and CoHb). In addition, iron-cobalt hybrid hemoglobin tetramers (Fe-Co hybrids) are synthesized by appropriate combinations of isolated subunit chains of FeHb and CoHb. By the use of the inherent differences in ligand specificity and affinity between Fe- and Co-containing hemoproteins, the mechanism of homotropic and heterotropic functions of hemoglobin will be elucidated by thermodynamic temperature-jump, stopped-flow, and flash-photolytic measurements of equilibria of FeHb, CoHb, and Fe-Co hybrids with ligands such as oxygen, carbon monoxide and alkyl isocyanides. Microscopic equilibrium and kinetic constants of their equilibria with such ligands are determined to deduce a pausible model of the cooperativity and allostery of hemoglobin, in which the subunit inequivalence is taken into account.